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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/introduction/introduction_ex2" target="_blank">Open introduction_ex2 in new tab.</a>
<a name="output"></a> 
<br><br><br> <h1> The console output of the program: </h1> 
<pre>
***************************************************************
* Running Example introduction_ex2:
*   example-opt  
***************************************************************
 
Running /Users/petejw/projects/libmesh_git/build/examples/introduction/introduction_ex2/.libs/example-opt

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=36
    n_local_nodes()=36
  n_elem()=25
    n_local_elem()=25
    n_active_elem()=25
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=2
   System #1, "Complex System"
    Type "Explicit"
    Variables={ "c" "T" } "dv" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" "MONOMIAL", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" "CARTESIAN" 
    Approximation Orders="FIRST", "THIRD" "SECOND", "THIRD" 
    n_dofs()=222
    n_local_dofs()=222
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=1
    n_matrices()=0
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 0
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 0
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0
   System #0, "Simple System"
    Type "TransientLinearImplicit"
    Variables="u" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" 
    Approximation Orders="FIRST", "THIRD" 
    n_dofs()=36
    n_local_dofs()=36
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=3
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.11111
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0


 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 09:50:45 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 -------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.006192, Active time=0.000507                                              |
 -------------------------------------------------------------------------------------------------------------
| Event                          nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                           w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-------------------------------------------------------------------------------------------------------------|
|                                                                                                             |
|                                                                                                             |
| DofMap                                                                                                      |
|   add_neighbors_to_send_list() 2          0.0000      0.000018    0.0000      0.000018    7.30     7.30     |
|   build_sparsity()             1          0.0001      0.000082    0.0001      0.000088    16.17    17.36    |
|   create_dof_constraints()     2          0.0000      0.000011    0.0000      0.000011    4.54     4.54     |
|   distribute_dofs()            2          0.0001      0.000044    0.0002      0.000106    17.16    41.81    |
|   dof_indices()                25         0.0000      0.000000    0.0000      0.000000    0.79     0.79     |
|   prepare_send_list()          4          0.0000      0.000000    0.0000      0.000000    0.39     0.39     |
|   reinit()                     2          0.0001      0.000063    0.0001      0.000063    24.65    24.65    |
|                                                                                                             |
| Mesh                                                                                                        |
|   find_neighbors()             1          0.0001      0.000098    0.0001      0.000098    19.33    19.33    |
|   renumber_nodes_and_elem()    2          0.0000      0.000002    0.0000      0.000002    0.79     0.79     |
|                                                                                                             |
| MeshTools::Generation                                                                                       |
|   build_cube()                 1          0.0000      0.000042    0.0000      0.000042    8.28     8.28     |
|                                                                                                             |
| Parallel                                                                                                    |
|   allgather()                  2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                             |
| Partitioner                                                                                                 |
|   single_partition()           1          0.0000      0.000003    0.0000      0.000003    0.59     0.59     |
 -------------------------------------------------------------------------------------------------------------
| Totals:                        45         0.0005                                          100.00            |
 -------------------------------------------------------------------------------------------------------------

 
***************************************************************
* Done Running Example introduction_ex2:
*   example-opt  
***************************************************************
 
***************************************************************
* Running Example introduction_ex2:
*   example-opt eqn_sys.dat 
***************************************************************
 
Running /Users/petejw/projects/libmesh_git/build/examples/introduction/introduction_ex2/.libs/example-opt eqn_sys.dat

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=36
    n_local_nodes()=36
  n_elem()=25
    n_local_elem()=25
    n_active_elem()=25
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=2
   System #1, "Complex System"
    Type "Explicit"
    Variables={ "c" "T" } "dv" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" "MONOMIAL", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" "CARTESIAN" 
    Approximation Orders="FIRST", "THIRD" "SECOND", "THIRD" 
    n_dofs()=222
    n_local_dofs()=222
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=1
    n_matrices()=0
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 0
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 0
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0
   System #0, "Simple System"
    Type "TransientLinearImplicit"
    Variables="u" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" 
    Approximation Orders="FIRST", "THIRD" 
    n_dofs()=36
    n_local_dofs()=36
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=3
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.11111
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

<<< Writing system to file eqn_sys.dat
>>> Reading system from file eqn_sys.dat

 EquationSystems
  n_systems()=2
   System #0, "Complex System"
    Type "Explicit"
    Variables={ "c" "T" } "dv" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" "MONOMIAL", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" "CARTESIAN" 
    Approximation Orders="FIRST", "THIRD" "SECOND", "THIRD" 
    n_dofs()=222
    n_local_dofs()=222
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=1
    n_matrices()=0
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 0
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 0
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0
   System #1, "Simple System"
    Type "TransientLinearImplicit"
    Variables="u" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" 
    Approximation Orders="FIRST", "THIRD" 
    n_dofs()=36
    n_local_dofs()=36
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=3
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.11111
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0


 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 09:50:45 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 -------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.006852, Active time=0.002378                                              |
 -------------------------------------------------------------------------------------------------------------
| Event                          nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                           w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-------------------------------------------------------------------------------------------------------------|
|                                                                                                             |
|                                                                                                             |
| DofMap                                                                                                      |
|   add_neighbors_to_send_list() 4          0.0001      0.000014    0.0001      0.000014    2.40     2.40     |
|   build_sparsity()             2          0.0001      0.000063    0.0001      0.000071    5.34     5.97     |
|   create_dof_constraints()     4          0.0000      0.000009    0.0000      0.000009    1.51     1.51     |
|   distribute_dofs()            4          0.0001      0.000033    0.0003      0.000082    5.55     13.75    |
|   dof_indices()                50         0.0000      0.000000    0.0000      0.000000    0.42     0.42     |
|   prepare_send_list()          8          0.0000      0.000000    0.0000      0.000000    0.08     0.08     |
|   reinit()                     4          0.0002      0.000048    0.0002      0.000048    8.16     8.16     |
|                                                                                                             |
| EquationSystems                                                                                             |
|   read()                       1          0.0006      0.000591    0.0012      0.001177    24.85    49.50    |
|   update()                     1          0.0000      0.000016    0.0000      0.000016    0.67     0.67     |
|   write()                      1          0.0004      0.000355    0.0004      0.000424    14.93    17.83    |
|                                                                                                             |
| Mesh                                                                                                        |
|   find_neighbors()             1          0.0001      0.000080    0.0001      0.000080    3.36     3.36     |
|   renumber_nodes_and_elem()    2          0.0000      0.000002    0.0000      0.000002    0.13     0.13     |
|                                                                                                             |
| MeshCommunication                                                                                           |
|   assign_global_indices()      2          0.0006      0.000318    0.0006      0.000321    26.79    27.04    |
|                                                                                                             |
| MeshTools::Generation                                                                                       |
|   build_cube()                 1          0.0000      0.000035    0.0000      0.000035    1.47     1.47     |
|                                                                                                             |
| Parallel                                                                                                    |
|   allgather()                  12         0.0000      0.000000    0.0000      0.000000    0.08     0.08     |
|   probe()                      24         0.0000      0.000000    0.0000      0.000000    0.42     0.42     |
|   receive()                    16         0.0000      0.000003    0.0000      0.000003    1.81     1.85     |
|   send()                       16         0.0000      0.000002    0.0000      0.000002    1.01     1.01     |
|   send_receive()               8          0.0000      0.000000    0.0000      0.000000    0.17     0.17     |
|                                                                                                             |
| Parallel::Request                                                                                           |
|   wait()                       16         0.0000      0.000001    0.0000      0.000001    0.71     0.71     |
|                                                                                                             |
| Partitioner                                                                                                 |
|   single_partition()           1          0.0000      0.000003    0.0000      0.000003    0.13     0.13     |
 -------------------------------------------------------------------------------------------------------------
| Totals:                        178        0.0024                                          100.00            |
 -------------------------------------------------------------------------------------------------------------

 
***************************************************************
* Done Running Example introduction_ex2:
*   example-opt eqn_sys.dat 
***************************************************************
</pre>
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